“He’s actually a lot better today,” coach Wade Phillips said Monday. “He’s really in a day-to-day situation as far as where he’s going to be as far as being able to play. … He took quite a hit, but has really bounced back strong. That’s encouraging for him and us.”

Phillips described the injury as a neck strain.

Ware spent several hours in the hospital Sunday after he was hurt in the fourth quarter of a 20-17 loss to the San Diego Chargers. Phillips said the linebacker went home that night.

Backup safety and special teams player Pat Watkins sprained his left knee on a kickoff return Sunday and will be out at least two weeks. Philips also said tight end Martellus Bennett has not been cleared to play after experiencing concussion-like symptoms that kept him out Sunday. Bennett will not play Saturday night at undefeated New Orleans.

The Cowboys are 8-5 and have dropped a game behind Philadelphia in the NFC East.

Ware was hurt while pursing quarterback Philip Rivers. The three-time Pro Bowl linebacker got around another offensive lineman and then went headfirst into the upper leg of lineman Brandyn Dombrowki. Ware remained on the ground for several anxious minutes, then was immobilized and strapped to a stretcher before being taken off the field.

In October, Ware agreed to a $78 million, six-year contract extension through the 2015 season that included a $20 million signing bonus. The 27-year-old was in the final year of the contract he signed after being selected with the 11th overall pick in the 2005 draft.